The inventive concept relates to encryption methods and related apparatuses. More particularly, the inventive concept relates to encryption methods and related apparatuses that make use of the Chinese Remainder Theorem (CRT) as applied to Rivest Shamir Adleman (RSA) encryption methods and apparatuses.
Representative calculations involved in the use of the certain RSA encryption methods include exponentiation operation(s) using a given “secret key”. Various adaptations to RSA encryption methods have been suggested to improve the efficiency of the exponentiation operations in environments where system resources (e.g., available memory space) used to perform certain calculations are limited. Among the these adaptations, the so-called Chinese Remainder Theorem (CRT) may be used to generate digital signature(s) at speeds approximately four times faster than previously used, unmodified RSA encryption methods and systems. This class of CRT modified RSA encryption methods and systems may be termed the “CRT-RSA approach” inclusive of CRT-RSA method(s) and/or CRT-RSA system(s).
Despite notable performance advantages, the CRT-RSA approach creates exploitable weaknesses in associated data processing operations. That is, CRT-RSA systems and computational methods are fairly weak against so-called “fault attacks”.